Antiferromagnetic Chain Research Articles

Defect-induced ferromagnetism in a S\u2009=\u20091/2 quasi-one-dimensional Heisenberg antiferromagnetic chain compound

We present evidences that defects in the spin S = 1/2 Heisenberg antiferromagnetic chain (HAFC) compound can lead to ferromagnetism by studying the magnetic and thermal properties of the newly discovered quasi-one-dimensional (1D) metal–organic framework [CH3NH3][Cu(HCOO)3] (MACuF). Our findings suggest that the long-range ferromagnetic order at 3.7 K can be attributed to Cu2+ ions from the 2D networks constructed by the endpoints of the broken chains. In such a case, the intrinsic magnetism can emerge in this quasi-1D Heisenberg chain system at the background of the short-range antiferromagnetism. This unusual ferromagnetism found in HAFC not only enriches magnetic features in the low-dimensional systems, but helps to understand some of the exotic magnetic phenomena in other real quasi-1D magnetic materials.

Holographic quantum algorithms for simulating correlated spin systems

We present a suite of ``holographic'' quantum algorithms for efficient ground-state preparation and dynamical evolution of correlated spin systems, which require far fewer qubits than the number of spins being simulated. The algorithms exploit the equivalence between matrix-product states (MPS) and quantum channels, along with partial measurement and qubit reuse, in order to simulate a $D$-dimensional spin system using only a $(D\ensuremath{-}1)$-dimensional subset of qubits along with an ancillary qubit register whose size scales logarithmically in the amount of entanglement present in the simulated state. Ground states can either be directly prepared from a known MPS representation or obtained via a holographic variational quantum eigensolver (holoVQE). Dynamics of MPS under local Hamiltonians for time $t$ can also be simulated with an additional (multiplicative) $\mathrm{poly}(t)$ overhead in qubit resources. These techniques open the door to efficient quantum simulation of MPS with exponentially large bond dimension, including ground states of two- and three-dimensional systems, or thermalizing dynamics with rapid entanglement growth. As a demonstration of the potential resource savings, we implement a holoVQE simulation of the antiferromagnetic Heisenberg chain on a trapped-ion quantum computer, achieving within $10(3)%$ of the exact ground-state energy of an infinite chain using only a pair of qubits.

The exact solution of magnetic susceptibility for finite Ising ring with a magnetic impurity

We connected the two ends of a finite spin-1/2 antiferromagnetic Ising chain with a magnetic impurity at one end to form a closed ring, and studied its magnetic susceptibility exactly by using the transfer matrix method. We calculated the magnetic susceptibility in the whole temperature range and gave the phase diagram at ground state of the system about the anisotropy of the impurity and strength of the connection exchange interaction for spin-1 and -3/2 impurities. We also gave the ground state entropy of the system and derived the asymptotic expression of the magnetic susceptibility multiplied by temperature at the zero-temperature limit and the high-temperature limit. It was found that a degenerate phase may exist in some parameter region at zero temperature for the odd spin number system, and the ground state entropy is ln(2) in the nondegenerate phase and is dependent on the spin number in the degenerate phase. The magnetic susceptibility of the system at low temperature exhibits ferromagnetic behavior, and the Curie constant is related to the spin configuration at ground state. When the ground state is nondegenerate, the Curie constant is equal to the square of the net spin, regardless of the parity of the number of the spin. When the spin number is odd and the ground state is degenerate, the Curie constant may be related to the total spin number. At the high-temperature limit, the magnetic susceptibility multiplied by temperature is related to the spin quantum number of the impurity and the spin number in the ring.

Quasi-one-dimensional uniform spin- 12 Heisenberg antiferromagnet KNaCuP2O7 probed by P31 and Na23 NMR

We present the structural and magnetic properties of KNaCuP$_2$O$_7$ investigated via x-ray diffraction, magnetization, specific heat, and $^{31}$P NMR and $^{23}$Na NMR measurements and complementary electronic structure calculations. The temperature dependent magnetic susceptibility and $^{31}$P NMR shift could be modeled very well by the uniform spin-$1/2$ Heisenberg antiferromagnetic chain model with nearest-neighbour interaction $J/k_{\rm B}\simeq 58.7$ K. The corresponding mapping using first principles electronic structure calculations leads to $J^{\rm DFT}/k_{\rm B} \simeq 59$ K with negligibly small inter-chain couplings ($J^{\prime}/k_{\rm B}$, $J^{\prime \prime}/k_{\rm B} < 0.1$ K), further confirming that the system is indeed an one-dimensional uniform spin-$1/2$ Heisenberg antiferromagnet. The temperature-dependent unit cell volume could be described well using the Debye approximation with a Debye temperature of $\Theta_{\rm D} \simeq 294$ K, consistent with the heat capacity data. The diverging trend of the NMR spin-lattice relaxation rates ($^{31}1/T_1$ and $^{23}1/T_1$) imply the onset of a magnetic long-range-ordering at very low temperatures supporting the anticipated $T_{\rm N} \simeq 0.38$ K from the inter-chain couplings. Moreover, the NMR spin-lattice relaxation rates show the dominant contributions from uniform ($q=0$) and staggered ($q = \pm \pi/a$) spin fluctuations in the high and low temperature regimes, respectively mimicking one-dimensionality of the spin-lattice. We have also demonstrated that $^{31}1/T_1$ in high temperatures varies linearly with $1/\sqrt{H}$ reflecting the effect of spin diffusion on the dynamic susceptibility. Further, the inter-chain frustration also substantially impede the magnetic ordering rendering the spin-lattice a perfect one-dimensional uniform spin-$1/2$ Heisenberg antiferromagnet over a wide temperature range.

From deconfined spinons to coherent magnons in an antiferromagnetic Heisenberg chain with long range interactions

We study the nature of the excitations of an antiferromagnetic (AFM) Heisenberg chain with staggered long range interactions using the time-dependent density matrix renormalization group method and by means of a multi-spinon approximation. The chain undergoes true symmetry breaking and develops long range order, transitioning from a gapless spin liquid to a gapless ordered AFM phase. The spin dynamic structure factor shows that the emergence of Néel order can be associated to the formation of bound states of spinons that become coherent magnons. The quasiparticle band leaks out from the two-spinon continuum that is pushed up to higher energies. Our physical picture is also supported by an analysis of the behavior of the excitations in real-time.

Mixed-order transition in the antiferromagnetic quantum Ising chain in a field

The antiferromagnetic quantum Ising chain has a quantum critical point which belongs to the universality class of the transverse Ising model (TIM). When a longitudinal field ($h$) is switched on, the phase transition is preserved, which turns to first-order for $h/\Gamma \to \infty$, $\Gamma$ being the strength of the transverse field. Here we will re-examine the critical properties along the phase transition line. During a quantum block renormalization group calculation, the TIM fixed point for $h/\Gamma>0$ is found to be unstable. Using DMRG techniques, we calculated the entanglement entropy and the spin-spin correlation function, both of which signaled a divergent correlation length at the transition point with the TIM exponents. At the same time, the bulk correlation function has a jump and the end-to-end correlation function has a discontinuous derivative at the transition point. Consequently for finite $h/\Gamma$ the transition is of mixed-order.

Curvature-driven homogeneous Dzyaloshinskii–Moriya interaction and emergent weak ferromagnetism in anisotropic antiferromagnetic spin chains

Chiral antiferromagnets are currently considered for a broad range of applications in spintronics, spin-orbitronics, and magnonics. In contrast to the established approach relying on materials screening, the anisotropic and chiral responses of low-dimensional antiferromagnets can be tailored relying on the geometrical curvature. Here, we consider an achiral, anisotropic antiferromagnetic spin chain and demonstrate that these systems possess geometry-driven effects stemming not only from the exchange interaction but also from the anisotropy. Peculiarly, the anisotropy-driven effects are complementary to the curvature effects stemming from the exchange interaction and rather strong as they are linear in curvature. These effects are responsible for the tilt of the equilibrium direction of vector order parameters and the appearance of the homogeneous Dzyaloshinskii–Moriya interaction. The latter is a source of the geometry-driven weak ferromagnetism emerging in curvilinear antiferromagnetic spin chains. Our findings provide a deeper fundamental insight into the physics of curvilinear antiferromagnets beyond the σ-model and offer an additional degree of freedom in the design of spintronic and magnonic devices.

Qubit Regularization of Asymptotic Freedom.

We provide strong evidence that the asymptotically free (1+1)-dimensional nonlinear O(3) sigma model can be regularized using a quantum lattice Hamiltonian, referred to as the "Heisenberg comb," that acts on a Hilbert space with only two qubits per spatial lattice site. The Heisenberg comb consists of a spin-half antiferromagnetic Heisenberg chain coupled antiferromagnetically to a second local spin-half particle at every lattice site. Using a world-line MonteCarlo method, we show that the model reproduces the universal step-scaling function of the traditional model up to correlation lengths of 200000 in lattice units and argue how the continuum limit could emerge. We provide a quantum circuit description of the time evolution of the model and argue that near-term quantum computers may suffice to demonstrate asymptotic freedom.

Generation of Current Vortex by Spin Current in Rashba Systems

Employing unbiased large-scale time-dependent density-matrix renormalization-group simulations, we demonstrate the generation of a charge-current vortex via spin injection in the Rashba system. The spin current is polarized perpendicular to the system plane and injected from an attached antiferromagnetic spin chain. We discuss the conversion between spin and orbital angular momentum in the current vortex that occurs because of the conservation of the total angular momentum and the spin-orbit interaction. This is in contrast to the spin Hall effect, in which the angular-momentum conservation is violated. Finally, we predict the electromagnetic field that accompanies the vortex with regard to possible future experiments.

A chromium(III) bis-acetylide complex containing a trans-diethyl-ethylenedithio-substituted tetrathiafulvalene (TTF) derivative: synthesis, crystal structures, and magnetic properties

A new Cr(III) bis-acetylide complex containing redox-active ethynyl-substituted 4-methyl-4′,5′-trans-diethyl-ethylenedithio-tetrathiafulvalene, [Cr(III)cyclam(C≡C-MeEt2EDT-TTF)2]n+ ([1]n+) was synthesized. The crystal structures of two salts, [1][Ni(dmit)2] (dmit = 2-thioxo-1,3-dithiole-4,5-dithiolate) and [1][Ni(mnt)2]3 (mnt = maleonitriledithiolate), were determined by single-crystal X-ray diffraction. In the crystal of [1][Ni(dmit)2], the trans-diethyl group of [1]+ is in the axial position and prevents π-stacking of the TTF units, resulting in a negligibly weak spin–spin interaction between Cr3+ and [Ni(dmit)2]−. In contrast, in [1][Ni(mnt)2]3, the trans-diethyl group is in the equatorial position in [1][Ni(mnt)2]3 owing to the strong attractive force between the π-stacked TTF+ units and the [Ni(mnt)2]− anions. This π-stacking has a significant effect on the magnetic property of [1] [Ni(mnt)2]3. The π-stacked TTF+ units and [Ni(mnt)2]− anions behave approximately as a one-dimensional S = 1/2 antiferromagnetic chain connecting the spins of Cr3+ antiferromagnetically.

Structural and magnetic properties of the quantum magnet BaCuTe2O6

We investigate the structural and magnetic properties of the new quantum magnet BaCuTe$_2$O$_6$. This compound is synthesized for the first time in powder and single crystal form. Synchrotron X-ray and neutron diffraction reveal a cubic crystal structure (P4$_1$32) where the magnetic Cu$^{2+}$ ions form a complex network. Physical properties measurements suggest the presence of antiferromagnetic interactions with a Curie-Weiss temperature of -33K, while long-range magnetic order occurs at the much lower temperature of ~6.3K. The magnetic structure, solved using neutron diffraction, reveals antiferromagnetic order along chains parallel to the a, b and c crystal axes. This is consistent with the magnetic excitations which resemble the multispinon continuum typical of the spin-1/2 Heisenberg antiferromagnetic chain. A consistent intrachain interaction value of ~34K is achieved from the various techniques. Finally the magnetic structure provides evidence that the chains are coupled together in a non-colinear arrangement by a much weaker antiferromagnetic, frustrated hyperkagome interaction.

Helimagnetism in MnBi2Se4 Driven by Spin-Frustrating Interactions Between Antiferromagnetic Chains

We report the magnetic properties and magnetic structure determination for a linear-chain antiferromagnet, MnBi2Se4. The crystal structure of this material contains chains of edge-sharing MnSe6 octahedra separated by Bi atoms. The magnetic behavior is dominated by intrachain antiferromagnetic (AFM) interactions, as demonstrated by the negative Weiss constant of −74 K obtained by the Curie–Weiss fit of the paramagnetic susceptibility measured along the easy-axis magnetization direction. The relative shift of adjacent chains by one-half of the chain period causes spin frustration due to interchain AFM coupling, which leads to AFM ordering at TN = 15 K. Neutron diffraction studies reveal that the AFM ordered state exhibits an incommensurate helimagnetic structure with the propagation vector k = (0, 0.356, 0). The Mn moments are arranged perpendicular to the chain propagation direction (the crystallographic b axis), and the turn angle around the helix is 128°. The magnetic properties of MnBi2Se4 are discussed in comparison to other linear-chain antiferromagnets based on ternary mixed-metal halides and chalcogenides.

Coupled spin- 12 antiferromagnetic chain Cs2LiRuCl6 with partially disordered crystal lattice

We determined the crystal structure of ${\mathrm{Cs}}_{2}{\mathrm{LiRuCl}}_{6}$, which was synthesized in this work, and investigated its magnetic properties. ${\mathrm{Cs}}_{2}{\mathrm{LiRuCl}}_{6}$ has a hexagonal structure composed of linear chains of face-sharing ${\mathrm{RuCl}}_{6}$ and ${\mathrm{LiCl}}_{6}$ octahedra. In two thirds of the structural chains, ${\mathrm{Ru}}^{3+}$ and ${\mathrm{Li}}^{+}$ sites are almost ordered, while in the other chains their sites are disordered. This situation is analogous to the ground state of the antiferromagnetic Ising model on a triangular lattice. Using electron paramagnetic resonance, we evaluated the $g$ factors of ${\mathrm{Ru}}^{3+}$ with effective spin-$\frac{1}{2}$ as ${g}_{c}\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}2.72$ and ${g}_{ab}\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}1.50$ for magnetic fields $H$ parallel and perpendicular to the $c$ axis, respectively. Magnetization curves for $H\ensuremath{\parallel}c$ and $H\phantom{\rule{0.16em}{0ex}}\ensuremath{\perp}\phantom{\rule{0.16em}{0ex}}c$ are highly anisotropic. However, these magnetization curves approximately coincide when normalized by the $g$ factors. It was found from the magnetization and specific heat results that ${\mathrm{Cs}}_{2}{\mathrm{LiRuCl}}_{6}$ can be described as a coupled one-dimensional $S\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}1/2$ Heisenberg-like antiferromagnet with $J/{k}_{\mathrm{B}}\phantom{\rule{0.16em}{0ex}}\ensuremath{\simeq}\phantom{\rule{0.16em}{0ex}}3.7$ K. Three-dimensional ordering occurs at ${T}_{\mathrm{N}}\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}0.48$ K. A magnetic phase diagram for $H\ensuremath{\parallel}c$ is also presented.

Quasi-one-dimensional magnetism in the spin- 12 antiferromagnet BaNa2Cu(VO4)2

We report synthesis and magnetic properties of quasi-one-dimensional spin-$\frac{1}{2}$ Heisenberg antiferromagnetic chain compound BaNa$_2$Cu(VO$_4$)$_2$. This orthovanadate has a centrosymmetric crystal structure, $C2/c$, where the magnetic Cu$^{2+}$ ions form spin chains. These chains are arranged in layers, with the chain direction changing by 62$^0$ between the two successive layers. Alternatively, the spin lattice can be viewed as anisotropic triangular layers upon taking the inter-chain interactions into consideration. Despite this potential structural complexity, temperature-dependent magnetic susceptibility, heat capacity, ESR intensity, and NMR shift agree well with the uniform spin-$1/2$ Heisenberg chain model with an intrachain coupling of $J/k_{\rm B} \simeq 5.6$ K. The saturation field obtained from the magnetic isotherm measurement consistently reproduces the value of $J/k_{\rm B}$. Further, the $^{51}$V NMR spin-lattice relaxation rate mimics the 1D character in the intermediate temperature range, whereas magnetic long-range order sets in below $T_{\rm N} \simeq 0.25$ K. The effective interchain coupling is estimated to be $J_{\perp}/k_{\rm B} \simeq 0.1$ K. The theoretical estimation of exchange couplings using band-structure calculations reciprocate our experimental findings and unambiguously establish the 1D character of the compound. Finally, the spin lattice of BaNa$_2$Cu(VO$_4$)$_2$ is compared with the chemically similar but not isostructural compound BaAg$_2$Cu(VO$_4)_2$.

Effect of a magnetic field in an S = 1 antiferromagnetic chain with single-ion anisotropy and alternating bonds with disorder

In this study, we investigated the quantization of magnetization at low temperatures in a spin-1 antiferromagnetic chain with single-ion anisotropy by considering the quenched disorder in alternating bonds. Each spin i interacts with its nearest neighbors via Ji and αJi couplings, where Ji is considered to obey a Gaussian or Bernoulli probability distribution function, with width σ. Zero temperature phase diagrams were obtained by minimizing the energy of the Hamiltonian. For finite temperatures, a transfer matrix technique was applied in order to treat the partition function. Consequently, the magnetization curve calculated by deriving the quenched average of the free energy exhibited interesting plateaus, which were modified when randomness was considered. Experimentally, these plateaus appear when some chain structures are subjected to a magnetic field.

Particle–hole symmetries in condensed matter

The term “particle–hole symmetry” is beset with conflicting meanings in contemporary physics. Conceived and written from a condensed-matter standpoint, the present paper aims to clarify and sharpen the terminology. In that vein, we propose to define the operation of “particle–hole conjugation” as the tautological algebra automorphism that simply swaps single-fermion creation and annihilation operators, and we construct its invariant lift to the Fock space. Particle–hole symmetries then arise for gapful or gapless free-fermion systems at half filling, as the concatenation of particle–hole conjugation with one or another involution that reverses the sign of the first-quantized Hamiltonian. We illustrate that construction principle with a series of examples including the Su–Schrieffer–Heeger model and the Kitaev–Majorana chain. For an enhanced perspective, we contrast particle–hole symmetries with the charge-conjugation symmetry of relativistic Dirac fermions. We go on to present two major applications in the realm of interacting electrons. For one, we offer a heuristic argument that the celebrated Haldane phase of antiferromagnetic quantum spin chains is adiabatically connected to a free-fermion topological phase protected by a particle–hole symmetry. For another, we review the recent proposal by Son [Phys. Rev. X 5, 031027 (2015)] for a particle–hole conjugation symmetric effective field theory of the half-filled lowest Landau level, and we comment on the emerging microscopic picture of the composite fermion.

High-field spin-flop state in green dioptase

The high-field magnetic properties and magnetic order of the gem mineral green dioptase Cu$_6[$Si$_6$O$_{18}]\cdot 6$H$_2$O have been studied by means of single-crystal neutron diffraction in magnetic fields up to $21~$T and magnetization measurements up to $30~$T. In zero field, the Cu$^{2+}$-moments in the antiferromagnetic chains are oriented along the $c$-axis with a small off-axis tilt. For a field applied parallel to the $c$-axis, the magnetization shows a spin-flop-like transition at $B^*=12.2~$T at $1.5~$K. Neutron diffraction experiments show a smooth behavior in the intensities of the magnetic reflections without any change in the periodicity of the magnetic structure. Bulk and microscopic observations are well described by a model of ferromagnetically coupled antiferromagnetic $XXZ$ spin-$\frac{1}{2}$ chains, taking into account a change of the local easy-axis direction. We demonstrate that the magnetic structure evolves smoothly from a deformed N\'eel state at low fields to a deformed spin-flop state in a high field via a strong crossover around $B^*$. The results are generalized for different values of interchain coupling and spin anisotropy.

Quantum fluctuation effects on the ordered moments in a two dimensional frustrated ferrimagnet

We propose a novel two-dimensional (2D) frustrated quantum spin-1/2 anisotropic Heisenberg model with alternating ferromagnetic and antiferromagnetic magnetic chains along one direction and antiferromagnetic interactions along the other. The (mean-field) ground state is ferrimagnetic in certain range of the interaction space. Spin-wave theory analysis of the reduction of ordered moments at inequivalent spin sites and the instability of the spin waves suggest a quantum phase transition which has the characteristics of both the frustrated 2D antiferromagnetic S = 1/2 (J 1, J 2) model and 1D S 1 = 1, S 2 = 1/2 quantum ferrimagnetic model.

Dynamical spin excitations of the topological Haldane gapped phase in the S=1 Heisenberg antiferromagnetic chain with single-ion anisotropy

We study the dynamical spin excitations of the one-dimensional $S=1$ Heisenberg antiferromagnetic chain with single-ion anisotropy by using quantum Monte Carlo simulations and stochastic analytic continuation of imaginary-time correlation function. Using the transverse dynamic spin structure factor, we observe the quantum phase transition with a critical point between the topological Haldane gapped phase and the trivial phase. At the quantum critical point, we find a broad continuum characterized by the Tomonaga-Luttinger liquid similar to a $S=1/2$ Heisenberg antiferromagnetic chain. We further identify that the elementary excitations are fractionalized spinons.

Identifying phase transition point of &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;-&lt;i&gt;J&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt; antiferromagnetic Heisenberg spin chain by machine learning

Studying quantum phase transitions through order parameters is a traditional method, but studying phase transitions by machine learning is a brand new field. The ability of machine learning to classify, identify, or interpret massive data sets may provide physicists with similar analyses of the exponentially large data sets embodied in the Hilbert space of quantum many-body system. In this work, we propose a method of using unsupervised learning algorithm of the Gaussian mixture model to classify the state vectors of the &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;-&lt;i&gt;J&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt; antiferromagnetic Heisenberg spin chain system, then the supervised learning algorithm of the convolutional neural network is used to identify the classification point given by the unsupervised learning algorithm, and the cross-validation method is adopted to verify the learning effect. Using this method, we study the &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;-&lt;i&gt;J&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt; Heisenberg spin chain system with chain length &lt;i&gt;N&lt;/i&gt; = 8, 10, 12, 16 and obtain the same conclusion. The first order phase transition point of &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;-&lt;i&gt;J&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt; antiferromagnetic Heisenberg spin chain system can be accurately found from the ground state vector, but the infinite order phase transition point cannot be found from the ground state vector. The first order and the infinite order phase transition point can be found from the first excited state vector, which indirectly shows that the first excited state may contain more information than the ground state of &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;-&lt;i&gt;J&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt; antiferromagnetic Heisenberg spin chain system. The visualization of the state vector shows the reliability of the machine learning algorithm, which can extract the feature information from the state vector. The result reveals that the machine learning techniques can directly find some possible phase transition points from a large set of state vectorwithout prior knowledge of the energy or locality conditions of the Hamiltonian, which may assists us in studying unknown systems. Supervised learning can verify the phase transition points given by unsupervised learning, thereby indicating that we can discover some useful information about unknown systems only through machine learning techniques. Machine learning techniques can be a basic research tool in strong quantum-correlated systems, and it can be adapted to more complex systems, which can help us dig up hidden information.